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Source Publication

Proceedings of the American Mathematical Society

Source ISSN

0002-9939

Original Item ID

doi: 10.1090/S0002-9939-1983-0715874-4; Shelves: QA1 .A5215 Storage S

Abstract

We answer some questions raised in [1]. In particular, we prove: (i) Let F be a compact subset of the euclidean plane E2 such that no component of F separates E2. Then E2\F can be partitioned into simple closed curves iff F is nonempty and connected. (ii) Let F Ç E2 be any subset which is not dense in E2, and let S be a partition of E2\F into simple closed curves. Then S has the cardinality of the continuum. We also discuss an application of (i) above to the existence of flows in the plane.